Field of the Invention
The invention relates to a method of producing a perforated mask having a desired pattern of perforations for the projection of particle radiation onto a projection area. The preferred field of application of the invention is the production of masks for electron or ion-beam lithography in the fabrication of integrated circuits, in particular, for the lithographic formation of very fine structures with dimensions below 130 nm.
To produce integrated circuits, various layers of selected semiconductor, conductor, and insulating materials are applied one after another to a wafer-like substrate, referred to as a wafer, and are each processed selectively in predefined areas to form fine structures in the layers. Lithographic processes configure the pattern of the respective structure, in that, radiation having an effect in the desired manner on the respective material to be treated is projected onto the relevant layer through a mask. The projection mask is constructed in accordance with the desired pattern so that only the areas to be treated are irradiated and the remaining areas are shielded from the radiation. The irradiated layer is normally a film of a xe2x80x9cresistxe2x80x9d material, whose irradiated areas are washed away after a development operation to expose the layer lying underneath selectively in accordance with the desired pattern and, therefore, to make it receptive to specific selective processing such as etching, semiconductor doping, vapor deposition.
The lithographic process that is most common at present is optical lithography (photolithography), which operates with optical irradiation. Projection masks for optical lithography include a carrier material that is transparent to the radiation used (in the case of transmission masks) or is reflective like a mirror (in the case of reflection masks) and bears a shielding layer in those portions of its area that are to let through or reflect no radiation to the object being exposed. The lower limit for the size of the structures that can be defined by optical projection is directly proportional to the wavelength of the light used and inversely proportional to the numerical aperture of the imaging system. With increasing miniaturization of integrated circuits, the development of optical lithography processes is, therefore, moving to shorter and shorter wavelengths as far as the ultraviolet (UV) range and even beyond that.
Although radiation in the UV range still permits projection techniques by optical lenses, it permits resolutions only down to a fineness of the order of magnitude of about 100 nm. To permit even smaller structure sizes, special projection techniques and masks for electromagnetic radiation in the X-ray range have been developed or proposed. Because, in the case of X-rays, no optical lenses can be used for the reduced imaging of a mask, the mask has to be formed as a xe2x80x9c1:1 maskxe2x80x9d on the same scale as the structures to be provided. In addition, because flooded exposure with an appropriately broad parallel X-ray beam cannot apply the necessary energy density to the irradiated area, the 1:1 mask, together with the wafer to be exposed, has to be subjected to a scanning movement relative to the source of a narrowly collimated X-ray beam, for example, relative to a synchrotron ring. X-ray lithography, therefore, requires a complicated and expensive apparatus and, because of the time-consuming mechanical scanning technique, is barely suitable for the mass production of integrated circuits.
In view of such a problem, more recent developments are aimed at implementing lithography for very small structures (for example below 130 nm) by particle radiation instead of by electromagnetic radiation. The particles to be used in such a case are electrons or ions that, because of their electric charge, can be accelerated and focused by electric or magnetic lenses so that reduced imaging of the mask pattern onto the projection area is also possible. With such particle radiation, much smaller structures can be formed on a projection area than by conventional optical radiation or by X-rays because the equivalent wavelength of electrons or ions is many times smaller than the wavelength of the shortest-wave electromagnetic radiation. Although no optical radiation is used in particle beam lithography, the expression xe2x80x9cexposurexe2x80x9d is commonly also used here for the selective irradiation procedure.
There are materials that are sufficiently sensitive to exposure with particles such as ions or electrons to form a useable resist for particle radiation lithography. On the other hand, there are no materials that are sufficiently transparent to ions to be able to serve as a transmitting carrier material for a projection mask. Although there are materials that are transparent to electrons, high transmission losses occur when they are used. Masks for ion projection lithography (IPL), therefore, have to be perforated masks, that is to say, to be of a diaphragm of a material that is opaque to the particles used and is perforated in accordance with the desired projection pattern. The use of such perforated masks is also desirable for electron projection lithography (EPL) to avoid the aforementioned transmission losses.
The narrower the mask openings formed by the perforation, the thinner must the diaphragm be so that the ratio of depth to width of the openings remains small. Lithography of small structures, therefore, requires very thin diaphragms. Furthermore, it is desirable to give the diaphragm as large an area as possible so that a sufficient number of pattern components-can be accommodated on it to cover an entire wafer by full area exposure and so that no time-consuming scanning or blockwise exposure of the wafer is necessary.
The required low thickness and the desired large area of the diaphragm, and also the presence of the perforation, leads to the mask having a relatively low stiffness with respect to mechanical stresses in the directions of its main plane. This means that longitudinal and shear forces in the directions of the main plane lead to distortions of the perforation pattern. Because the requirements on the accuracy of placement of the mask openings become higher and higher as the size of the exposure structures decreases, calculation of all the mechanical distortions that occur is necessary. To be able to calculate the distortions exactly in advance and compensate for them, both the stresses that act and the actual stiffness of the perforated diaphragm must be made available in all areas.
The mechanical stresses depend on parameters of the production process and also on external influences, for example, on the mounting, on thermal effects, ion implantation and so on, and may be predicted quantitatively or determined empirically. The stiffness of the diaphragm, on the other hand, is not only a function of the material and of the thickness but also depends on the shape of the perforation pattern, that is to say, on the form, the size, and the density of the mask openings, and can, therefore, be very different from place to place within the diaphragm. If the actual stiffness of the diaphragm and its local fluctuations have been determined, this information, together with the information about the mechanical stresses, can be used to calculate the distortion that occurs, by the method of xe2x80x9cfinite elementsxe2x80x9d (FE method).
The FE method is a model calculation in which the overall area to be investigated is broken down into a finite number of adjacent polygonal xe2x80x9ccellsxe2x80x9d, and the relevant elasticity values for each cell are determined numerically, namely, the modules of elasticity, the shear modulus, and the Poisson""s ratio in the plane considered. The values determined for each cell are linked with those of the adjacent cells and with the mechanical stress that acts to determine the relative displacement of the corners of the cells vectorially. The vector array so obtained describes the distortion of the overall area. Suitable FE methods are in the prior art and, therefore, do not need to be described more extensively at this point; a reference to the relevant specialist literature suffices, for example, K. J. Bathe, xe2x80x9cFinite Elemente Methodenxe2x80x9d, Springer 1986, O. C. Zienkiewicz, The Finite Element Method, 3rd edition, McGraw Hill.
For the numerical determination of the elasticity values of a cell, in each case a sufficiently large data set must be provided to-describe the part of the perforation pattern of the diaphragm located within the cell sufficiently accurately. For example, for a cell whose dimensions are 0.25xc3x970.25 mm on the diaphragm, a data set of up to 1 Gbyte is needed, of which the processing for the numerical determination of the elasticity values lasts about 1 day when a current industrial computer is used. Such a time is unreasonably long because the total area of the perforation pattern of a diaphragm may be 100xc3x97100 mm, for example, if full-field exposure of a chip area of the normal size of 25xc3x9725 mm is to be carried out on a wafer with a reduced imaging scale of 1:4.
To determine the local distribution of the stiffness of a perforated diaphragm to be used as a perforated mask with reduced computing effort, an empirical function has been determined for specific geometries, which contains the xe2x80x9copening ratioxe2x80x9d of the diaphragm as a parameter, that is to say, the ratio of the sum of the cross-sectional areas of all the mask openings to the total area of the mask (cf. the publication by G. A. Frisque et al., which appeared in the Proceedings of 1999 SPIE Symposium on Emerging Lithographic Technologies III, pages 768-778). Specifically, in the method disclosed, a unit load is applied to an xe2x80x9celementary cellxe2x80x9d of a pattern and the average stiffness is calculated by using the distortion response determined by FE calculation. An FE calculation is then carried out again, in which the periodically repeating elementary cells are replaced by elements of average stiffness (equivalent stiffness). For particularly symmetrical structures (square arrays in a quadratic outline), an analytical solution for the average stiffness is specified.
However, such a method can be used only for highly symmetrically, isotropically distributed structures. To determine the stiffness distribution of perforated mask diaphragms with complicated anisotropic structures, one has hitherto, therefore, always been directed toward the numerical calculation of the cells. Because of the immense computing effort, such a method cannot be applied to the complete construction of an integrated circuit of normal size.
It is accordingly an object of the invention to provide a method of producing a perforated mask for particle radiation that overcomes the hereinafore-mentioned disadvantages of the heretofore-known devices and methods of this general type and that carries out production within a tolerable time period even in the case of complicated anisotropic structures of the mask pattern.
With the foregoing and other objects in view, there is provided, in accordance with the invention, a method of producing a perforated mask having a desired pattern of openings for a projection of particle radiation onto a projection area, including the steps of cutting openings in a blank broadened in two dimensions, after the cutting, subjecting the blank to deformation forces leaving a distortion of an expected cut pattern, calculating the distortion in advance by determining values of an elasticity of adjacent cells of the mask with respect to longitudinal and shear stresses in a main plane of the mask on a model having the desired pattern of openings, calculating the vector field of the expected distortion by linking the elasticity values determined with the deformation forces with a FE calculation, selecting a pattern for cutting the blank, the pattern representing the desired pattern with a distortion being an inverse of the calculated distortion, determining geometric variables including a length and a direction of all edge sections of each of the openings and a cross-sectional area of each of the openings by measuring openings of each of the cells of at least a selected subset of cells of the model, and analytically determining the elasticity values of each selected cell from preselected functions containing, as a variable, statistical parameters derived from the determined geometric variables.
In the method according to the invention, therefore, no complicated numerical calculation of the elasticity values of all the cells by time-consuming FE methods is carried out; instead, the average elasticity values of the cells are determined by a statistical analysis and preselected mathematical functions, which can be found empirically. The values of the statistical parameters to be used in such a case can be determined relatively simply and quickly, and their linking with the empirical function requires only a little computing time in each case so that the entire procedure only lasts for a few seconds for each cell (as compared with 1 day in the case of numerical elasticity calculation). The empirical mathematical functions, after they have been determined once, apply in unchanged form to virtually all possible patterns; therefore, only the values of the listed statistical parameters have to be determined as pattern specific variables.
The elasticity values of the cells, determined in a simplified way according to the invention, form the basis for the subsequent FE model calculation for the prior determination of the distortions. In spite of the simplification, this prior determination can be sufficiently accurate.
The invention is based on the novel finding that there is a relatively small set of statistical parameters in the physical structure of a perforated mask that, taken on their own, are sufficient to determine the elasticity values of limited mask areas sufficiently accurately, even for complicated anisotropic structures, and, in that, to calculate the elasticity values, generally applicable mathematical functions may be found that contain only these parameters as a variable. The invention includes the technical implementation of such a finding by specifying a limited number of specific and easily measurable geometric variables, from which the statistical parameters are to be derived to carry out the distortion correction in the course of mask production by using the elasticity information calculated therefrom.
In accordance with another mode of the invention, the edge sections are assumed as being edges of a smallest-area rectangle circumscribing a relevant one of the openings.
In accordance with a further mode of the invention, the following statistical parameters are derived from the geometric variables determined for each of a number of discrete directional areas: a opening ratio equal to a ratio of a sum of cross-sectional areas of all the openings to a total area; an orientation parameter indicating what proportion of the sum of greater edge lengths of the openings falling in a directional area is of the sum of all the greater edge lengths of the openings; and an edge length parameter indicating what proportion of the sum of the edge lengths falling in the directional area is of the sum of all the edge lengths.
In accordance with an added mode of the invention, the moduli of elasticity Ex and Ey in an X direction and a Y direction orthogonal thereto, a shear modulus Gxy in the XY plane, and a Poisson""s ratio Qxy in the XY plane are determined from the following functions:
Ex=E[P(V)+P(Oy)+P(Ky)]; 
Ey=E[P(V)+P(Ox)+P(Kx)]; 
Gxy=G[P(V)+P(Ox)+P(Ky)]; and 
Qxy=P(V)+P(Ky) 
where:
P is a respective polynomial of a variable indicated in brackets of the functions; and
E=a modulus of elasticity of a material of the mask blank;
G=a shear modulus of the material of the mask blank;
V=1xe2x88x92(the opening ratio);
Ox=an orientation parameter for the X direction;
Oy=an orientation parameter for the Y direction;
Kx=an edge length parameter for the X direction; and
Ky=an edge length parameter for the Y direction.
In accordance with an additional feature of the invention, Ex, Ey, Gxy, and Qxy are determined with the functions:                                           E            x                    =                      [                                                            a                  i                                ·                V                            +                                                a                  2                                ·                                  V                  2                                            +                                                a                  3                                ·                                  V                  3                                            +                                                a                  4                                ·                                  (                                      0.5                    -                                          O                      y                                                        )                                            +                                                a                  5                                ·                                                      (                                          0.5                      -                                              O                        y                                                              )                                    2                                            +                                                a                  6                                ·                                                      (                                          0.5                      -                                              O                        y                                                              )                                    3                                            +                                                a                  7                                ·                                  (                                      0.5                    -                                          K                      y                                                        )                                                      ]                          ;            ⁢              
            ⁢                                    E            y                    =                      E            ⁡                          [                                                                    b                    1                                    ·                  V                                +                                                      b                    2                                    ·                                      V                    2                                                  +                                                      b                    3                                    ·                                      V                    3                                                  +                                                      b                    4                                    ·                                      (                                          0.5                      -                                              O                        x                                                              )                                                  +                                                      b                    5                                    ·                                                            (                                              0.5                        -                                                  O                          x                                                                    )                                        2                                                  +                                                      b                    6                                    ·                                                            (                                              0.5                        -                                                  O                          x                                                                    )                                        3                                                  +                                                      b                    7                                    ·                                      (                                          0.5                      -                                              K                        x                                                              )                                                              ]                                      ;            ⁢              
            ⁢                                    G            xy                    =                      G            ⁡                          [                                                                    c                    1                                    ·                  V                                +                                                      c                    2                                    ·                                      V                    2                                                  +                                                      c                    3                                    ·                                      V                    3                                                  +                                                      c                    4                                    ·                                      (                                          0.5                      -                                              O                        x                                                              )                                                  +                                                      c                    5                                    ·                                                            (                                              0.5                        -                                                  O                          x                                                                    )                                        2                                                  +                                                      c                    6                                    ·                                                            (                                              0.5                        -                                                  O                          x                                                                    )                                        3                                                  +                                                      c                    7                                    ·                                      (                                          0.5                      -                                              K                        y                                                              )                                                              ]                                      ;        and            ⁢              
            ⁢                        Q          xy                =                                            d              1                        ·            V                    +                                    d              2                        ·                          V              2                                +                                    d              3                        ·                          V              3                                +                                    d              4                        ·                          (                              0.5                -                                  O                  x                                            )                                +                                    d              5                        ·                                          (                                  0.5                  -                                      O                    x                                                  )                            2                                +                                    d              6                        ·                                          (                                  0.5                  -                                      O                    x                                                  )                            3                                +                                    d              7                        ·                          (                              0.5                -                                  k                  y                                            )                                            ]    ,  and
the coefficients a1 to a7, b1 to b7, c1 to c7, and d1 to d7 are empirically determined. Preferably, in accordance with a concomitant feature of the invention:
xe2x88x9217.81xe2x89xa6a1xe2x89xa6xe2x88x9211.87;
+31.08xe2x89xa6a2xe2x89xa6+46.62;
xe2x88x9229.78xe2x89xa6a3xe2x89xa6xe2x88x9219.86;
xe2x88x922.36xe2x89xa6a4xe2x89xa6xe2x88x921.58;
+3.94xe2x89xa6a5xe2x89xa6+5.92;
+0.46xe2x89xa6a6xe2x89xa6+0.70;
+4.21xe2x89xa6a7xe2x89xa6+6.31;
+5.65xe2x89xa6b1xe2x89xa68.47;
xe2x88x9223.80xe2x89xa6b2xe2x89xa6xe2x88x9215.86;
+12.15xe2x89xa6b3xe2x89xa6+18.23;
xe2x88x923.49xe2x89xa6b4xe2x89xa6xe2x88x922.33;
xe2x88x9226.75xe2x89xa6b5xe2x89xa6xe2x88x9217.83;
+30.39xe2x89xa6b6xe2x89xa6+45.59;
+6.22xe2x89xa6b7xe2x89xa6+9.37;
+7.89xe2x89xa6c1xe2x89xa6+11.83;
xe2x88x9232.50xe2x89xa6c2xe2x89xa6xe2x88x9221.66;
+15.09xe2x89xa6c3xe2x89xa6+22.63;
xe2x88x922.11xe2x89xa6c4xe2x89xa6xe2x88x921.41;
+2.15xe2x89xa6c5xe2x89xa6+3.23;
xe2x88x928.12xe2x89xa6c6xe2x89xa6xe2x88x925.42;
xe2x88x923.12xe2x89xa6c7xe2x89xa6xe2x88x922.08;
+44.72xe2x89xa6d1xe2x89xa6+67.08;
xe2x88x92168.04xe2x89xa6d2xe2x89xa6xe2x88x92122.02;
+69.80xe2x89xa6d3xe2x89xa6+104.70;
xe2x88x9216.25xe2x89xa6d4xe2x89xa6xe2x88x9210.83;
+16.60xe2x89xa6d5xe2x89xa6+24.90;
xe2x88x9275.64xe2x89xa6d6xe2x89xa6xe2x88x9250.42; and
xe2x88x9226.83xe2x89xa6d7xe2x89xa6xe2x88x9217.89.
Other features that are considered as characteristic for the invention are set forth in the appended claims.
Although the invention is illustrated and described herein as embodied in a method of producing a perforated mask for particle radiation, it is, nevertheless, not intended to be limited to the details shown because various modifications and structural changes may be made therein without departing from the spirit of the invention and within the scope and range of equivalents of the claims.
The construction and method of operation of the invention, however, together with additional objects and advantages thereof, will be best understood from the following description of specific embodiments when read in connection with the accompanying drawings.